$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}7&54\\24&55\end{bmatrix}$, $\begin{bmatrix}13&18\\2&45\end{bmatrix}$, $\begin{bmatrix}15&20\\54&25\end{bmatrix}$, $\begin{bmatrix}55&46\\34&15\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.48.0-56.g.1.1, 56.48.0-56.g.1.2, 56.48.0-56.g.1.3, 56.48.0-56.g.1.4, 56.48.0-56.g.1.5, 56.48.0-56.g.1.6, 56.48.0-56.g.1.7, 56.48.0-56.g.1.8, 168.48.0-56.g.1.1, 168.48.0-56.g.1.2, 168.48.0-56.g.1.3, 168.48.0-56.g.1.4, 168.48.0-56.g.1.5, 168.48.0-56.g.1.6, 168.48.0-56.g.1.7, 168.48.0-56.g.1.8, 280.48.0-56.g.1.1, 280.48.0-56.g.1.2, 280.48.0-56.g.1.3, 280.48.0-56.g.1.4, 280.48.0-56.g.1.5, 280.48.0-56.g.1.6, 280.48.0-56.g.1.7, 280.48.0-56.g.1.8 |
Cyclic 56-isogeny field degree: |
$32$ |
Cyclic 56-torsion field degree: |
$768$ |
Full 56-torsion field degree: |
$129024$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 2 x^{2} - 3 x y + 2 y^{2} + 56 z^{2} $ |
This modular curve has no real points, and therefore no rational points.
Hi
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Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.